Final Report Essentials

Author

Affiliation

Jeremy Springman

University of Pennsylvania

Index Variables

Simple Additive Index

• Measured on the same scale
• Share direction

Adding numberical measures

Count of times a respondent…

• q13_4_1: Contacted gov’t official
• q13_6_1: Contacted a student representative
• q13_7_1: Contacted an NGO

  [1]  0  3  1  0  1  5  1  4  0  1  2 10  0  2  0  3  4  0  3  1  2  1  0  5  1
 [26]  0  7  6 10  4  0  1  2  4  0  0  3  0  4  1  0  0  0  0  0  1  0  1  1  4
 [51]  4  0  0  3  0  4  3  1  1  0  4  8  0  0 11  5  1  0  0  1  0  0  0  0  1
 [76]  1  1  3  4  1  3  3  2  1  5  1  7  0  0  2  0  2  6  1  0  2  1  4  0  2
[101]  1  0  3  2  2  0  1  0  0  1  2  5  0  4  1  2  0  1  0  0  2  0  7  2  7
[126]  3  0  0  6  0  2  2  0  0  6  0  0  0  5  1 17  2  9  1  1  2  0  2  1  1
[151] 13  0  0  2  1 14  0  1  8  0  1  0  0  9  1  0  6  5  1  0  4  2  0  0  3
[176]  3  3  0  1  0  1  0  0  0  2  5  2  0  5  4  2  2  1  2  1  0  0  0  1  1
[201]  0  4 18  3  0  1  1  0  1  0  7 17  2  0  2  0  3  2  0  1  1  0  0  9  0
[226]  0  1  0  1  0  1  2  0  1  2  1  2  6  0  0  1  0  1  2  4  0  1  0  7  0
[251]  3  1  0  1  3 20  0  2  4  2  0  0  3  0  1  0  2  1  0  0  8 14  2  7  0
[276]  0  0  3  0  2  5  4  5  0  0  2  5  0  2  0  3  0  0 10  1  1  3  9  1  0
[301]  6  1  0  2  2  2  0  0  7  6  2  8  2  0  5 13  1  1  2  0  1  0  4  3  0
[326]  0  0  1  1  3  1  1  0  3  0  0  7 12  0  0  2  1  6  6  1  0  0 10  1  0
[351]  4  0  5  5  1  1  0  6  5  0  0  1  0  0  1  2  4  2  2  0  3  0  3  5  5
[376]  4  0  0 17  6  0  0  0  5  5  0 13  0  2  1  0  3 11  1  0  2  2  1  0  0
[401]  1  1  5  2  0  0  3  0  3  0  0  2  1  4  0  0  3  1  3  3  0  0  0  2  0
[426]  1  3  5  7  5  0  0  0 11  5  0  3  1  2  0  1  1  0  3  0  1  1  0  0  3
[451]  0  6  2  0  3  5  1  0  0  4  0  7  1  2  1  3  1  3  0  2  4  0  1  2  0
[476]  3  5  5  1  0  0  0  0  5  0  0  1  0  0  1  0  1 13  6  0  0  0  2  0  5
[501]  2  1  5  1  1  2  0  0  8  0  0  0  0  1  0  3  4  1  2  0  0  5  0 30  1
[526]  2  2  4  2  0  0  7  0  2  2  3  0  0  3  0  0  0  1  1  1  6  5  1  2  0
[551]  1  0  6  0  0  0  5  2  0  0  0  0  2  0  0  5  3  3  1  2 10  5  0  3  5
[576]  4  1  2  2  0  2  0  2  0  1  2  0  8  4 15  1 13  2  1  3  4  1  0  2  0
[601]  8  3  3  0  4  0  0  0  1  1  5  0  1  9  0  0  2  1  1  3  0  3  0  1  4
[626]  2  0  0  1  4  7  3  2 13  0  0  1  1  0  2  0 13  0  0  0  2  0  0  0  1
[651]  0  1  1  2  1  4  0  4  0  0  3  1  7  4  4  0  2  0  3  3  2  1  0  4  0
[676]  9  9  2  0  3  2  0 11  1  0  7  0  0  0  3 18  3  1  0  1  2  2  1  3  0
[701]  5  1  6  2  2  1  6  0  0  4  0  0  0  2  0  3  3 12  5  0  0  8  1  4  1
[726]  0  6  0  1  1  0  0  0  2  0  0  0  3  2  3  0  1  2  1  0  3  0  3  0  1
[751] 10  2  2  3  0  0  1  3  0  2  8  5  0  0  2  3  4  1  3  0  0  0  3  3  0
[776]  6  0  0  1 14  4  3  2  2  0  0  8  3 32  3  2  0  2  2  0  0  0  2  9  0
[801]  2  1  3  0  0  2  5  2  0  0  3  5  0  3  1  0  6  0  3  3  0  0  2  3  0

Do they ‘hang together’?

[1] 0.4910388

Visualizing the result

Thinking about weights

Stretching the concept…

What if we wanted to add the count of times a respondent…

• q13_5_1: Signed a petition

[1] 0.6121334

Adding likert measures

• q16_1: Intention to join religious group
• q16_2: Intention to join ethnic interest group
• q16_3: Intention to join political party
• q16_4: Intention to join voluntary org

Averaged Z-Scores

• \(Z = (X - \mu) / \sigma\)
• \(z_i = \frac{X_i - \bar{X}}{s}\)
• Standardized: Mean of 0 and standard deviation of 1

Interaction Terms

Differences across groups

Binary

  Year I  Year II Year III 
     327      277      221 

  0   1 
327 221 

	Multivariate	Interaction
(Intercept)	−0.14** (0.05)	−0.18** (0.06)
moved	0.27*** (0.06)	0.33*** (0.07)
year	−0.05 (0.05)	0.04 (0.09)
moved × year		−0.14 (0.11)
Num.Obs.	534	534
R2 Adj.	0.045	0.046

Continuous-ish

  0   1   2 
327 277 221 

	Bivariate	Multivariate	Interaction
(Intercept)	−0.150*** (0.036)	−0.121** (0.045)	−0.169** (0.056)
moved	0.234*** (0.045)	0.228*** (0.045)	0.301*** (0.067)
year		−0.029 (0.027)	0.019 (0.042)
moved × year			−0.080 (0.054)
Num.Obs.	809	809	809
R2 Adj.	0.032	0.032	0.033

More complex

  0   1   2 
327 277 221 

	Bivariate	Multivariate	Interaction
(Intercept)	−0.150*** (0.036)	−0.114* (0.046)	−0.184** (0.060)
moved	0.234*** (0.045)	0.232*** (0.045)	0.334*** (0.072)
year2		−0.060 (0.049)	0.077 (0.092)
year3		−0.053 (0.054)	0.038 (0.085)
moved × year2			−0.194+ (0.109)
moved × year3			−0.142 (0.110)
Num.Obs.	809	809	809
R2 Adj.	0.032	0.031	0.033

Differences over time

Cross-Sectional

	Bivariate	Multivariate	Interaction
(Intercept)	−0.179*** (0.023)	−0.165*** (0.027)	−0.150*** (0.033)
moved	0.257*** (0.029)	0.257*** (0.029)	0.234*** (0.041)
time		−0.027 (0.027)	−0.058 (0.047)
moved × time			0.046 (0.057)
Num.Obs.	1625	1625	1625
R2 Adj.	0.047	0.047	0.047

Fixed Effects

	Simple	Fixed Effects	Interaction
(Intercept)	0.005 (0.020)	−0.319** (0.115)	−0.294* (0.115)
time	−0.027 (0.028)	−0.028*** (0.008)	−0.059*** (0.014)
moved			−0.033 (0.162)
moved × time			0.047** (0.017)
Num.Obs.	1625	1625	1625
R2 Adj.	0.000	0.916	0.917